7x^2+10x-4=x^2-15x+5

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Solution for 7x^2+10x-4=x^2-15x+5 equation:


Simplifying
7x2 + 10x + -4 = x2 + -15x + 5

Reorder the terms:
-4 + 10x + 7x2 = x2 + -15x + 5

Reorder the terms:
-4 + 10x + 7x2 = 5 + -15x + x2

Solving
-4 + 10x + 7x2 = 5 + -15x + x2

Solving for variable 'x'.

Reorder the terms:
-4 + -5 + 10x + 15x + 7x2 + -1x2 = 5 + -15x + x2 + -5 + 15x + -1x2

Combine like terms: -4 + -5 = -9
-9 + 10x + 15x + 7x2 + -1x2 = 5 + -15x + x2 + -5 + 15x + -1x2

Combine like terms: 10x + 15x = 25x
-9 + 25x + 7x2 + -1x2 = 5 + -15x + x2 + -5 + 15x + -1x2

Combine like terms: 7x2 + -1x2 = 6x2
-9 + 25x + 6x2 = 5 + -15x + x2 + -5 + 15x + -1x2

Reorder the terms:
-9 + 25x + 6x2 = 5 + -5 + -15x + 15x + x2 + -1x2

Combine like terms: 5 + -5 = 0
-9 + 25x + 6x2 = 0 + -15x + 15x + x2 + -1x2
-9 + 25x + 6x2 = -15x + 15x + x2 + -1x2

Combine like terms: -15x + 15x = 0
-9 + 25x + 6x2 = 0 + x2 + -1x2
-9 + 25x + 6x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-9 + 25x + 6x2 = 0

Factor a trinomial.
(-9 + -2x)(1 + -3x) = 0

Subproblem 1

Set the factor '(-9 + -2x)' equal to zero and attempt to solve: Simplifying -9 + -2x = 0 Solving -9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x = 0 + 9 -2x = 0 + 9 Combine like terms: 0 + 9 = 9 -2x = 9 Divide each side by '-2'. x = -4.5 Simplifying x = -4.5

Subproblem 2

Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333

Solution

x = {-4.5, 0.3333333333}

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