3m+4=5m(m+3)

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Solution for 3m+4=5m(m+3) equation:


Simplifying
3m + 4 = 5m(m + 3)

Reorder the terms:
4 + 3m = 5m(m + 3)

Reorder the terms:
4 + 3m = 5m(3 + m)
4 + 3m = (3 * 5m + m * 5m)
4 + 3m = (15m + 5m2)

Solving
4 + 3m = 15m + 5m2

Solving for variable 'm'.

Combine like terms: 3m + -15m = -12m
4 + -12m + -5m2 = 15m + 5m2 + -15m + -5m2

Reorder the terms:
4 + -12m + -5m2 = 15m + -15m + 5m2 + -5m2

Combine like terms: 15m + -15m = 0
4 + -12m + -5m2 = 0 + 5m2 + -5m2
4 + -12m + -5m2 = 5m2 + -5m2

Combine like terms: 5m2 + -5m2 = 0
4 + -12m + -5m2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.8 + 2.4m + m2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 2.4m + 0.8 + m2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 2.4m + m2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 2.4m + m2 = 0 + 0.8
2.4m + m2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
2.4m + m2 = 0.8

The m term is 2.4m.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4m + 1.44 + m2 = 0.8 + 1.44

Reorder the terms:
1.44 + 2.4m + m2 = 0.8 + 1.44

Combine like terms: 0.8 + 1.44 = 2.24
1.44 + 2.4m + m2 = 2.24

Factor a perfect square on the left side:
(m + 1.2)(m + 1.2) = 2.24

Calculate the square root of the right side: 1.496662955

Break this problem into two subproblems by setting 
(m + 1.2) equal to 1.496662955 and -1.496662955.

Subproblem 1

m + 1.2 = 1.496662955 Simplifying m + 1.2 = 1.496662955 Reorder the terms: 1.2 + m = 1.496662955 Solving 1.2 + m = 1.496662955 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + m = 1.496662955 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + m = 1.496662955 + -1.2 m = 1.496662955 + -1.2 Combine like terms: 1.496662955 + -1.2 = 0.296662955 m = 0.296662955 Simplifying m = 0.296662955

Subproblem 2

m + 1.2 = -1.496662955 Simplifying m + 1.2 = -1.496662955 Reorder the terms: 1.2 + m = -1.496662955 Solving 1.2 + m = -1.496662955 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + m = -1.496662955 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + m = -1.496662955 + -1.2 m = -1.496662955 + -1.2 Combine like terms: -1.496662955 + -1.2 = -2.696662955 m = -2.696662955 Simplifying m = -2.696662955

Solution

The solution to the problem is based on the solutions from the subproblems. m = {0.296662955, -2.696662955}

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