2a*2a+3=7a

Solution for 2a*2a+3=7a equation:

Simplifying
2a * 2a + 3 = 7a

Reorder the terms for easier multiplication:
2 * 2a * a + 3 = 7a

Multiply 2 * 2
4a * a + 3 = 7a

Multiply a * a
4a2 + 3 = 7a

Reorder the terms:
3 + 4a2 = 7a

Solving
3 + 4a2 = 7a

Solving for variable 'a'.

Reorder the terms:
3 + -7a + 4a2 = 7a + -7a

Combine like terms: 7a + -7a = 0
3 + -7a + 4a2 = 0

Factor a trinomial.
(3 + -4a)(1 + -1a) = 0

Subproblem 1
Set the factor '(3 + -4a)' equal to zero and attempt to solve:

Simplifying
3 + -4a = 0

Solving
3 + -4a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -4a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4a = 0 + -3
-4a = 0 + -3

Combine like terms: 0 + -3 = -3
-4a = -3

Divide each side by '-4'.
a = 0.75

Simplifying
a = 0.75
Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1a = 0 + -1
-1a = 0 + -1

Combine like terms: 0 + -1 = -1
-1a = -1

Divide each side by '-1'.
a = 1

Simplifying
a = 1
Solution
a = {0.75, 1}